Question: Rewrite as a simplified fraction. ${2.3\overline{39} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2339.3939...\\ 10x &= 23.3939...\end{align*}}$ Subtracting the two equations, we have: ${990x = 2316}$ ${x = \dfrac{2316}{990}} $ ${x = \dfrac{386}{165}} \text{or} {2 \dfrac{56}{165}}$